Simplify the following expression: $t = \dfrac{36q^3 - 36q^2}{36q^3 - 99q^2}$ You can assume $q \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $36q^3 - 36q^2 = (2\cdot2\cdot3\cdot3 \cdot q \cdot q \cdot q) - (2\cdot2\cdot3\cdot3 \cdot q \cdot q)$ The denominator can be factored: $36q^3 - 99q^2 = (2\cdot2\cdot3\cdot3 \cdot q \cdot q \cdot q) - (3\cdot3\cdot11 \cdot q \cdot q)$ The greatest common factor of all the terms is $9q^2$ Factoring out $9q^2$ gives us: $t = \dfrac{(9q^2)(4q - 4)}{(9q^2)(4q - 11)}$ Dividing both the numerator and denominator by $9q^2$ gives: $t = \dfrac{4q - 4}{4q - 11}$